Anomalous fluctuations in phases with a broken continuous symmetry

TL;DR

This paper demonstrates that Goldstone modes from broken continuous symmetries cause anomalously large fluctuations in the order parameter below T_c, with specific scaling behaviors and observable effects in neutron scattering experiments.

Contribution

It reveals the impact of Goldstone modes on order parameter fluctuations and susceptibility scaling, providing new insights into phase fluctuations in systems with broken continuous symmetry.

Findings

Variance of magnetization scales as L^4 in 2<d<4

Longitudinal susceptibility diverges as 1/q^{4-d}

Dynamic structure factor shows a critical continuum above spin wave pole

Abstract

It is shown that the Goldstone modes associated with a broken continuous symmetry lead to anomalously large fluctuations of the zero field order parameter at any temperature below T_c. In dimensions 2<d<4, the variance of the extensive spontaneous magnetization scales as L^4 with the system size L, independent of the order parameter dynamics. The anomalous scaling is a consequence of the 1/q^{4-d} divergence of the longitudinal susceptibility. For ground states in two dimensions with Goldstone modes vanishing linearly with momentum, the dynamical susceptibility contains a singular contribution (q^2-\omega^2/c^2)^{-1/2}. The dynamic structure factor thus exhibits a critical continuum above the undamped spin wave pole, which may be detected by neutron scattering in the N\'eel-phase of 2D quantum antiferromagnets.